INTERACTION OF KINDERGARTEN AND FAMILY IN THE MATHEMATICAL DEVELOPMENT OF PRESCHOOLERS

The relevance of the study of the interaction of kindergarten and family in the mathematical development of preschoolers is due to the fact that the unification of the family and kindergarten in one educational space implies the cooperation of teachers and parents. The mathematical development of preschool children will be successful if the teacher interacts with parents. Only cooperation between the kindergarten and the family can ensure the effectiveness of educational activities in the mathematical development of a preschool child. It is necessary to select the forms and methods of organizing this interaction, taking into account the age characteristics of children and the settings of the Federal State Educational Standard (complex tasks, integration of different types of activities, individualization of the child's mathematical development, etc.) in the mathematical development of preschool children. The work of a preschool teacher on the mathematical development of children is particularly time-consuming and requires a lot of pedagogical attention. Mathematical knowledge of preschoolers, such as counting down to ten in ascending and descending order; the ability to recognize numbers in a row and randomly, quantitative (one, two, three...) and ordinal (first, second, third...); to study and present the basic geometric shapes (triangle, square, circle, and others); the basic forms of measurement: the ability to measure length, volume, width, height using a conditional measurement measure; comparison of objects: heavier-lighter, larger-smaller, wider-narrower, higher-lower; the ability to navigate in space and time, etc., will later be the basis for school education.

How We Understand Hilbert’s Thought of Infinity

We know that Hilbert’s thought of infinity has profoundly influenced and changed the mathematical development of the 20th century, and yet there is inherent contradiction in his thought of infinity itself, building his understanding of infinity on Kant’s intuition and the principle of finalism. This paper analyzes his thought of infinity based on Hegel’s view of dialectical infinity, and points out the incompleteness of his understanding of infinity.

Cultural Heritage Restoration of a Hemispherical Vault by 3D Modelling and Projection of Video Images with Unknown Parameters and from Unknown Locations

Reverse engineering applied to architectural restoration for the reconstruction of structural surfaces depends on metric precision. Sometimes there are elements on these surfaces whose value is even higher than the building itself. This is the case for many churches whose ceilings have pictorial works of art. Reconstruction requires the existence of some identifiable remainder and/or a surface geometry that enables mathematical development. In our case, the vault has an irregular hemispherical geometry (without possible mathematical development), and there are no significant remains of the painting (which was destroyed by a fire). Through the 3D modelling of the irregular vault and two historic frames with a camera of unknown geometry, an inverse methodology is designed to project the original painting without metric deformations. For this, a new methodology to locate the camera positions is developed. After, a 3D virtual mathematical model of the complete image on the vault is calculated, and from it, partial 3D virtual images are automatically calculated depending on the variable unknown positions of the video cannons (distributed along the upper corridor of the apse) that will project them (visually forming a perfect complete 3D image).

Home Numeracy and Preschool Children’s Mathematical Development: Expanding Home Numeracy Models to Include Parental Attitudes and Emotions

Most studies suggest that home numeracy is correlated with preschool children’s current mathematical performance, and also predicts their mathematical performance longitudinally. However, this finding is not universal, and some studies do not suggest a close relationship between home numeracy and preschoolers’ mathematical development. There are several possible reasons for the discrepant findings, including the exact nature of numeracy activities provided, and possible unreliability of parental reports of home numeracy. However, parental attitudes might also lead to differing results: because attitudes might influence actual home numeracy provision or the ways in which it is reported; because parental attitudes and beliefs might be transmitted intergenerationally; and because parental mathematics anxiety may interact with home numeracy activities to create early negative emotional associations about mathematics, as some research suggests to be the case with regard to school-age children. There has been a significant amount of research in the first two of these areas, but very little in the third area with regard to preschoolers. It should be seen as an important area for further research.